Giovinazzi qualified eighth at the last street race in Baku and finished in the same place in FP2 behind Kevin Magnussen on Wednesday.
The Italian is hopeful that the form and consistency will continue over to qualifying for a chance at a decent grid position for the race to score points for the first time this season.
Giovinazzi said on the F1 site: “It was a positive day, all the team did a fantastic job.
“The car was easy to drive already from FP1, so yeah, really happy for today.
“We need to push really hard – try to find the last tenths, because still the midfield is really close.
"So we have to work really hard [on Friday] and make sure we are still in the top 10 also on Saturday.
“I hope to be in Q3 and then that would be a lot more easy on Sunday as well, so this is the target!”
Team principal Fred Vasseur was also satisfied with work done during the practice sessions but also didn’t want to think too far ahead to what it could mean.
“We are satisfied with the work we did today but we are not getting carried away,” said Vasseur.
“Finding some extra performance is crucial if we want to target two places in Q3, which is our objective.
“It’s good to start in Monaco with two clean sessions, as track time is essential to build confidence around this track.”